GATE Engineering Mathematics: Differential Equations: First order equations, Higher order linear differential equations, Variation of parameters, Cauchy and Euler equations, Partial differential equations, Separation of variables – Previous Year Questions

7 GATE previous year questions on Differential Equations: First order equations, Higher order linear differential equations, Variation of parameters, Cauchy and Euler equations, Partial differential equations, Separation of variables (Engineering Mathematics, Electrical Engineering) with answers and explanations, from every paper.

1. GATE 2017 EE Q37 (2 marks, Multiple choice) – Consider the differential equation (t2 - 81)dydt + 5ty = (t) with y(1) = 2. There exists a unique solution for this differential equation when t…
2. GATE 2019 EE Q13 (1 mark, Multiple choice) – The partial differential equation 2u t2-c2(2u x2+2u y2)=0;where c0 is known as
3. GATE 2020 EE Q26 (1 mark, Numerical answer) – Consider the initial value problem below. The value of y at x=2, (rounded off to 3 decimal places) is . dydx=2x-y, y(0)=1
4. GATE 2023 EE Q34 (1 mark, Numerical answer) – In the following differential equation, the numerically obtained value of y(t), at t=1, is (Round off to 2 decimal places). dydt=e- t2+ t,=0.01\ and\…
5. GATE 2024 EE Q45 (2 marks, Multiple select) – Which of the following differential equations is/are nonlinear?
6. GATE 2025 EE Q54 (2 marks, Numerical answer) – Consider ordinary differential equations given by x 1(t)=2x 2(t) x 2(t)=r(t) with initial conditions x 1(0)=1 and x 2(0)=0. If…
7. GATE 2026 EE Q14 (1 mark, Multiple choice) – Consider the following differential equation: t2d2ydt2+7tdydt+8ty=10(t) Which one of the following options is correct?